a dollar and 2-sixths of a dollar?have more than Peter? 10. How many 12ths of a mile 13. Which is most 3-fifths of a is of a mile? 1-sixth of a mile?rod, or 2-thirds of a rod? How and 1-sixth of a mile? ¡much? 11. What part of a mile are 14. What part of a shilling are of a mile and of a mile? Ans. 1-sixth of a shilling and 1-seventh is 3-sixths and is 2-sixths; 3-jof a shilling? sixths and 2-sixths are 5-sixths. 15. Whath is the sum of 1-6th 12. How much more is than and 1-7th? the differnce of 1-6th 1-sixth? jand 1-7th? 13. James gave to Peter of an 16. What part of an apple are apple, and to George 2-sixths of 1-3d, 1-4th and 1-5th of an apple? an apple, how much did he give to 2-5ths, 1-6th and 1-7th? 1-7th, both? What part of the apple had 2-8ths and 5-10ths? he left? How much did Georgel 30. By the preceding article gain if we divide the terms of 3. it has been seen that fractions 12ths by 3 the quotient is also ; must be brought to express simi- thus we have 4-16ths and 3-12ths lar parts of the same whole, or, in reduced to the common denominother words, must be reduced to a ator 4. The same may often be common denominator, and then effected by multiplying the terms we may add or subtract the nu-jof one or both the fractions. merators as whole numbers. 7. Reduce 5-10ths and 11-15ths When it is not readily seen what to a common denominator? 3-7ths the common denominator is, one and 6-21? 1-5th, and 16-20ths? may alway be found by multiply- 8. What is the sum of 5-10ths ing all the denominators together, and 11-15ths? 3-7ths and 6-21? 1. is how many tenths? 1-5th, 4-10ths and 16-20ths? 2. One fifth is how many tenths? 9. What is the difference be3. Reduce and 1-5th to a com-tween 5-10ths and 11-15ths? 3mon denominator. 7ths and 6-21? 4. Find a common denominator] 10. Peter had 3-7ths of a pear for 1-third and 2-5ths? 3-4ths and and gave 2.9ths of what he had to 2-6ths? 1-4th and 6-8ths? 1-7th George, what part of a pear had and 3-14ths? he left? 5. What is the sum of and 11. 2-9ths of 3-7ths is what part 2-5ths? 3-4ths and 2-6ths? 1-4th of 1? and 6-8ths? 2-7ths and 3-14ths? 12. is how many 4ths? 6ths? 6. What is a common denomin-8ths? 10ths? 12ths? 16ths? 20ths? ator of 3-12ths and 4-16ths? 13. is how many 6ths? 9ths? The numerator and denomina-27ths? 24ths? 15ths? 12ths? 18ths? tor of a fraction are called its 81ths? terms. If both the terms of a 14. is how many 8ths? 12ths? fraction be multiplied, or divided 16ths? 20ths? 27ths? 28ths? 32nds? by the same number, the value of 16.and are how many 4ths? the fraction is not altered. Thus, 8ths? 12ths? 20ths? 24ths? 16ths? if we divide the terms of 4-16ths) 17. 2-thirds and 1-6th are how (Ex. 6) by 4 the quotient is 1-4th, many 6ths? 12ths? 18ths? 24ths? and 1-4th is equal to 4-16ths. A-130ths? 36ths? 31. 1. A man bought 24|make one dollar there will be as pounds tea of one man for 24 dol-many dollars as 20s in 199, or 9 Jars, and 5 pounds of another for 19-20th dollars. Hence to find 5 dollars, how much did he buy? the value of an improper fraction What did it cost? in a whole or mixed number, we 2. In 2 how many halves? Ans.have only to divide the numera5 halves, or 5-2. tor by the denominator; the quo3. In 2 3-4ths how many 4ths?tient will be the whole number, Ans. 11-4ths. and the remainder, if any, placed 4. When is a fraction called over the denominator will be the answer required. improper? 5. Is 11-4ths a proper or an improper fraction? 16. A person divided a dollar between four beggars, to the first 6. Reduce 4 3-7ths to an im- he gave half of a dollar, to the proper fraction. 7. Reduce 6 4-5ths to an proper fraction. second a quarter, to the third one im-sixth, and the rest to the fourth, what part of a dollar did the 4th 8. In 11 how many thirds? Ans. receive? How many cent did each 33 thirds. ¡receive? 9. Why? Because, as there are 3 thirds in one, there must be 11 times 3 thirds or 33 thirds in 11. 10. In 20 how many 4ths? 5ths? 6ths? 17. A boy gave to another boy half of an apple, to another one third, another one fourth, and to another one fifth of an apple, how much did he give away in the 11. Reduce 4 2-thirds to an im- whole? proper fraction 18. How many 1-60ths are , 1, 12. Reduce 123-5ths to an im- and 1-5th? Ans. 77-60ths or proper fraction. 117-60ths. 13. Reduce 4 and 5 1-5th to 19. How many guineas are 2 improper fractions-to a common 1-5th guineas, 33-5ths and 5 1-5th denominator-and find their sum, guineas? 14. 4 3-5ths and 5 1-5th are how many 20ths? 15. In 199-20ths of a dollar how many dollars? Ans. As 20-20ths 20. 2 1-6ths, 3 3-5ths and 5 15ths are how many 1-30ths? 21. 65-30ths, 108-30ths and 121-30ths are how many 1s? 32. 1. A boy paid away sev-| 5. John is half as old as James, en cents, which were half of all he and James a third as old as Ruhad; how much had he? fus, whose age is 30 years; how 2. A boy gave 5 apples to his old is James? how old is John? sister, which were one third of 6. A post is one eighth in the all he had; how many had he at mud and six feet above it; what first? is its length? 3. A man spilled 4 gallons of 7. A post is four sixths in the brandy, which were two thirds of mud and 10 feet above it; what all he had; how much had he? is its length? If four sixths are in 4. Sarah is 6 years old, which the mud, two sixths are above it. is one quarter the age of her el-If two sixths are 10 feet, 4 sixths dest sister; what is the sister's are 20 feet, and 10 and 20 are 30. age Ans 8. In a certain school 12 study ter learn arithmetic, I sixth learn geography, which are one third of grammar, and 6 learn geography; the scholars; how many scholars how many scholars are there? are there? 12. What numher is that from 9. A post is one quarter in the which if 5 be subtracted 2 thirds mud, one half in the water, and 5 of the remainder will be four? feet above the water; what is its 13. What number is that which length? being increased by 1 half and 1 10. A post is one sixth in mud, third, itself will be 22? one third in water, and 12 feet a- 14. What number is that whose bove the water; what is its length? third part exceeds its sixth part by 11. In a certain school 1 third three? whose part exceeds its 8th of the pupils learn to read, I quar-part by 4? SECTION V. OF THE DIFFERENT DENOMINATIONS OF MONEY, TIME, WEIGHTS, AND MEASURES IN COMMON USE. 4 farthings, qrs. make 1 penny, d grs. 4 pence 1shill. pound 66 1 shilling, s. 48 12 12 pence MONEY. 1 33. The above denominations of gold, the eagle, half-eagle, and of Federal Money are authorized quarter-eagle, five of silver, the by the laws of the United States, dollar, half-dollar, quarter-dollar, but in the transaction of business dime and half-dime, and two of we seldom hear any of them men-copper, the cent and half-cent. tioned but dollars and cents. Of the small foreign coins current Hence the following may be use-jin the United States, the most comful. mon are the N. E. four pence half 25 cts. make 1 quarter of a dollar. penny or N. Y. sixpence worth 50 cts. 66 1 half of a dollar. 6 1-4 cepts, the N. E. ninepence, 75 cts. 66 3 quarters of a dollar. for N. Y. shilling worth 12 1-2 100 cts. 66 1 dollar. cents, the pistareen worth 20 cents, A coin is a piece of metal stamp-land the half-pistareen worth 10 ed, and having a legal value. The cents. The value of the several coins of the United States are three denominations of English money. 365 ds. 6 hrs. 1 year, yr. 31557600 525960|8766|3651| is different in different places. A 10. How many shillings in one dollar is reckoned 4s. 6d. in Eng-pound? 2? 4? 6? 32 5? ?? land, 5s. in Canada, 6s. in New- 11. How many shillings in half England, Virginia and Kentucky, a pound? one fourth? 8a. in New-York, Ohio and North 12. How many half cents in a Carolina, 7s. 6d. in Pennsylvania, dime? 2? 3? 5? 4? 6? New-Jersey, Delaware and Maryland, and 4s. 8d. in South-Caroli-pence half-pennies? na and Georgia. QUESTIONS. 1. How many mills in one cent? 2? 3? 4? 5? 6? 7? 2. How many cents in 1 dime? 2? 3? 4? 5? 6? 7? 8? 9? 3. How many dimes in one dollar? 2 3 4 5? 6? 7? 8? 9? 4. How many dollars in one gle? 2?? 4?5? 6? 7? 8? 9? 13. How many cents in 2 four 14. How many cents in 2 ninepences? 3? 4? 6? 8? 15. How many ninepence in a half dollar? in a dollar? 16. How many pistareens in one dollar? 2?3? . 17. What is a coin? What are the gold coins of the U. S.? the silea-ver coins? the copper coins? and the value of these coins in Federal 5. Ilow many cents in half a Money? dime? a dime and a half? 18. Name some of the foreign 6. How many cents in one dol-coins and their values? Jar? half dollar? quarter? 19. How is a dollar reckoned in 7. How many dollars in a half English money in different places? eagle? in a quarter? 8. How many farthings in penny? 2: 4? 3? 5? 7? 6? 9. How many pence in ling? 2? 4?3?5? 7? 6? months. No. days. No. 20. Repeat the tables of money one and the contractions by which the denominations are denoted. shil-! 21. How is Federal Money denoted? TIME. 34. The year is commonly di-year. Such years are called Bisvided into 12 months, as in the fol-sextile or Leap years. To know lowing table, called Calendar whether any year is a common or Leap-year, divide it by 4, if nothdays.ing remain, it is Leap-year, but if 311, 2 or 3 remain, it is 1st 2d or 3d 31 after Leap-year. The number of 30 days in the several months may be 31 called to mind by the following 30 verse. 31 July 6 28 August 7 31 Sept. 8 30 October 9 31 Nov. 10 30 Dec. 11 Jan. 0 WEIGHTS. IV. TROY WEIGHT. 24 grains, grs. make 1 penny weight, put.grs.24 pwts. Iloz.tlb.. 20 penny weights" 1 ounce, 12 ounces " 1 pound, 02. 480 20 3 lb. 5760 240 12 r V. APOTHECARIES WEIGHT. 20 grains gr. make 1 scruple, sc.grs.20. sc. 1|drms. [oz/lb 3 scruples. 8 drams 12 ounces. 8 1 66. 1 dram, dr. 60 31 1-i 96 12 1 Which hath twenty-eight, nay) 3. How many minutes in one more, quarter of an hour? one half hour? Hath twenty-nine one year in four. one third of an hour? one hour and The true solar year consists of a half? 365 days 5 h. 48 m. 57 s. or nearly 4. How many hours in 2 days? to 365: 1-4 days. A common year 5. How many days in 2 weeks? is 365 days, and one day is added in 3? 4? 5?:6? 6. How many days in a year? 7. Into how many months is the preceding years. This method of year usually divided? 8. What are they called? 13. How can you ascertain 44 m. 12s. This amounted to one whether any year is a leap year or day in about 130 years. To cor-not.. rect this error, Pepe Gregory, in 14. Repeat the verse by which 1582, ordered that ten days should the number of days in each month be struck out of the Calendar, by may be called to mind. calling the 5th of October the 15th; 15. What is the true length of and to prevent its recurrence, he the solar year? ordered that each succeeding cen- 16. What is meant by the Ju tury, divisible by 4, as 16 hundred, lian, or Old Style? 18. What was the consequence? 20 hundred and 24 hundred, should 17. How much does this differ be Leap years, but that the cen- from the true year? turies not divisible by 4, as 17 hundred, 18 hundred and 19 hundred, should be common years. 19. Who corrected it? 20. What was the new reckon This reckoning is called the Greg-ing called? orian or New Style. The New 21. What was done to keep the Style differs now twelve days from same season upon the same day of the old style. QUESTIONS. the month for the future? 22. What would the difference now be between the old and new 1. Repeat the table of time.. 2. How many seconds in two style? minutes? halfa minute? one fourth] of a minute? 23. Is the present year a bissex tile or common year? |